The size of graphs with given feedback vertex number (Q2127624)

In this paper, the study of the feedback number and the forest number of graphs are continued by extending the results of \textit{L. Shi} and \textit{H. Xu} [J. Graph Theory 85, No. 4, 759--779 (2017; Zbl 1368.05034)]. The authors establish sharp upper and lower bounds for the size of connected graphs with fixed order and feedback number. Corresponding extremal graphs are also characterized. As a corollary, they give a sharp lower bound for the forest number of a graph in terms of its order and size. The results are strong and interesting.